CSA don't charge a fee. Your maintenance should be 20% of your earnings, they'll calculate it for you. It'll be lower if you have other children but your debts aren't your daughter's fault, are they?
I can't advise about paying off items, could you not return them if they're not what you want or too expensive?
Difficult as it may seem, you have to let go of this anger towards her mum and your feeling you 'should' have unsupervised contact. At this age and in your circumstances, it's not something that is a right I'm afraid.
Could you ask to come along next time your ex takes your daughter swimming? Or ask that she or her mum come along while you take her swimming?
Honestly, I wouldn't've let my son's father take him off swimming at 6 months without me, and we had a fairly amicable relationship. The very last thing you should be saying is "I'd love to put her in the car and take her"... anywhere! It could be twisted to sound bad. You need to be as inclusive as possible. Without reproach, you know?
Honestly you have no idea how grim forced contact/contact centers can be for the child and the father. Concentrate on making sure she knows you, help out as much as you can. Is the three hours each weekend day or spread between? Could you ask for it to be increased?
Basically, the more reasonable requests you make (why not via email, then you will have evidence), with no trace at all of any ill feeling towards the mother, will stand you in good stead IF you decide to go the legal route.
Things will either get better or they won't, but if the mother remains (in your view), unfairly denying you access, you won't have a leg to stand on if you present stuff like your posts to the courts, especially if the mum claims you've been aggressive/the baby hardly knows you/you are reluctant to pay maintenance etc (I am not saying any of this is true, but it needs to be demonstrably not true, you know?)
It really will just be an hour a week in a contact center then.
You can't make the baby's mother want to be with you, it doesn't sound like you like her much anyway, so let it go and concentrate on being a good father.
For now, the mum is her main carer, she gets to call the shots and that really IS fair with such a small baby in the circumstances you are in.
You will need to learn terms like "non-resident parent" too. I am bowing out now as I can find threads like this quite triggering after my own experiences, but good luck!